On the computation of the straight lines contained in a rational surface

Juan Gerardo Alcázar, Jorge Caravantes

Published 2016-03-12Version 1

In this paper we present an algorithm to compute the real and complex straight lines contained in a rational surface, defined by a rational parametrization. The algorithm relies on the well-known theorem of Differential Geometry that char- acterizes real straight lines contained in a surface as curves that are simulta- neously asymptotic lines, and geodesics. We also report on an implementation carried out in Maple 18. Examples and timings show the efficiency of the algo- rithm for moderate degrees, compared with a brute-force approach.